So Sarang is a sociopath and seok is a psycopath right? Or are they both sociopath ? But s...

Neither. Sarang is a mental illness and Seok cares about his image a lot.

so much so to a point it can be classed as obsessive which is a mental disorder in itself
Sarang I think has psychopathy
Seok I think has some form of OCPD but on the high functioning spectrum

I’m not a psychologist so obviously take this with a grain of salt, but based on Sarang’s traits such as:
A lack of empathy and emotional depth
Manipulativeness and deceitfulness
Impulsivity and irresponsibility
An inability to form genuine emotional relationships
A lack of guilt, shame, or moral conscience
I would categorize her as a psychopath. Which is a personality disorder under the umbrella of Antisocial Personality Disorder (ASPD)

"Sociopathy" is a term that describes a number of characteristic traits that fit the criteria of Antisocial Personality Disorder (ASPD), so you would say "that person has sociopathic traits/tendencies", while "psychopathy" is a colloquial (daily, everyday) term, and it just means the same thing as sociopathy/sociopath.
Psychopathy is to sociopathy like dick is to penis

But what about when she cried? She's shown a lot of emotions regarding her dead mom, which makes me think she doesn't have ASPD

it is a spectrum plus although it might not be derived from grief or mourning it can still evoke emotions coming from other places like just the fear of being left with her dad, I dont think she blames her mum for dying and leaving her in this situation but I think she still feels some form of emotion (just not love or loss)

Does labeling this or that so important? It is reductive.

I suppose so, but it's fun chatting about it and discussing stuff